Margaret Hodge, chair of the public accounts committee, told the executives of G4S and Serco: 'I think you should be dropped until the SFO has finished its inquiries.' Photograph: Pa

Margaret Hodge has accused the government of "shocking complacency" after it emerged that two outsourcing firms being investigated for alleged fraud over Ministry of Justice deals worth more than £200m have been bidding for further contracts while potentially facing criminal charges.

The chair of the public accounts committee said it was "utterly extraordinary" that G4S and Serco were allowed to do so while being investigated over contracts worth more than £200m by the Serious Fraud Office and the City of London.

Three G4S contracts worth more than £110m are being investigated by the SFO. They are a Ministry of Justice contract to administer tagging of prisoners on probation as well as two contracts for the management of "invoicing, delivery and performance reporting".

One Serco contract worth more than £40.5m is under investigation by the SFO. Another contract for the escort of prisoners to and from courts worth £49.3m is being investigated by City of London police.

"I am strongly of the view that we should not award new contracts for the two companies until we have established the facts about both their performance and their corporate behaviour.

"That is why I have requested an audit of every contract that MoJ holds with G4S and Serco," he said.

But executives from both firms told the committee on Monday that they had both put together bids for more government contracts since inquiries by the authorities began.

Hodge said in response: "I am shocked … Shocked that this can carry on. I think you should be dropped until the SFO has finished its inquiries. I do wonder what on earth the government is doing dealing with you if you are not, as you say, too big to fail."

"You have been found to have overcharged. In these cases if you are not too big to fail it is best to say 'hang on'," she said.

Peter Neden, the regional UK and Ireland president of G4S, said his company had continued to put forward bids for contracts but had not been awarded any during that time.

Rupert Soames, the group chief executive of Serco, said the government was restricted in what it could do by EU law. "I understand that part of the problem around an outright ban was a ban under EU law which we would not have challenged anyway … We did not win any new business," he said.

The multimillion-pound tagging scandal, which emerged in July 2013, triggered a Cabinet Office review of all government contracts worth more than £10m held by G4S and Serco.

Observers have claimed that there are very few other firms large enough or willing to bid for this type of work if Serco and G4S are excluded.

A National Audit Office report last week found that poor management of £40bn worth of outsourced public contracts had left the government exposed to the possibility of widespread fraud and overcharging.

A test sample of 60 government contracts found that 34 – more than half – had "issues in the amount billed".

Auditors also tested 73 contracts against a good practice framework and found many elements of the deals were at "material risk" of overbilling, but the problem could be far wider.

Departments relied on the information supplied by the outsourcing companies rather than carrying out their own checks, according to the report.

It also found that in some government departments no one could say which civil servant, if any, was in charge of making sure that an outsourcing firm was honouring a particular contract.